We answer a question from Raghavan and SteprÄns
by showing that $\mathfrak{s} = {\mathfrak{s}}_{\omega, \omega}$. Then we use this to construct a completely separable maximal almost disjoint family under $\mathfrak{s} \leq \mathfrak{a}$, partially answering a question of Shelah.

A $Q$-set is a set of reals every subset of which is a relative
$G_\delta$. We investigate the combinatorics of $Q$-sets and
discuss a question of Miller and Zhou on the size $\qq$ of the smallest
set of reals which is not a $Q$-set. We show in particular that various
natural lower bounds for $\qq$ are consistently strictly smaller than
$\qq$.